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posted by maths .
(a) Find the indeﬁnite integrals of the following functions.
(i) f (t) = 6 cos(3t) + 5e^−10t
(ii) g(x) = 2112x^3/ x (x > 0)
(iii) h(u) = cos^2( 1/8 u)
(b) Evaluate: (this big F sign at the start, 5 at the top and 1 at the bottom)
5 1/4x (7 + 6x^2) dx
F
1
(c)
(i) Write down a deﬁnite integral that will give the value of the area under the curve y = x^2 cos(2x) between x = 3/4 pie and x = pie.
(You are not asked to evaluate the integral by hand.)
(ii) ﬁnd the area described in part (c)(i), giving your
answer correct to three decimal places
MY ANSWERS:
for a) ii)
6cos (3t) dx = 4sin (3t) + c
5e^10t dx = 1/5 e^10t + c
ii) g (x) = 21 12x^3 / x (x>0)
diverse through by x
g (x) = 21/ x  12x^3
21/ x  12x^3 dx = 12Ln x  x^4 + c
iii) h (u) = cos^2 (1/8u)
using the second version of the double angled formula for cos (2delta)
=1/2 cos (2x 1/8 u) + 1/2 du
= 1/2 / 28 sin (2/8u) + 1/2 x + c
= 6/4 sin (2/8u) + 1/2u + c
i don't know whether that's right, and i don't know how to do the rest.
could some body please help me out. thanks!
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